Synthetic fibers usually have glass transition temperatures (also called second-order transition temperatures), and at temperatures lower than these temperatures, polymer molecules are frozen and molecular movement becomes difficult. Therefore, when drawing such fibers, usually the drawing temperature is the glass transition point of the fibers or higher and the drawing procedure is carried out in conditions such that the polymer molecules are easily movable. When a synthetic fiber is forcibly drawn while the polymer molecules of the fiber are frozen at the glass transition temperature or lower, however, the polymer molecules will not be oriented, and accordingly, fibers exhibiting a specific touch entirely different from that of the drawn fibers of the prior art are obtained (note, if the frozen polymer molecules are forcibly drawn by the method of the prior art, stretching irregularities will be inevitably formed, and thus a product having a uniform appearance cannot be obtained). Therefore, the drawing of synthetic fibers at a temperature corresponding to the glass transition temperature thereof or lower is the same as that used in the process for production of the Thick & Thin fiber, as also shown in Japanese Patent Publication (Kokoku) No. 58-44762, and accordingly, it is impossible to obtain only a specific touch without generating drawing irregularities. Also, since this drawing at the glass transition point or lower forcibly stretches the frozen polymer molecules, a very strong force is required therefor and thus many problems arise in that slippage of the filaments occurs at peripheral surfaces of the rollers, which leads to fluffs and the generation of laps. Also, a problem arises in that the productivity of the drawn filament yarn is lowered.